Missed this one. For sure I have failed, and so largely have you guys, except perhaps HappySkeptic. It's a matter of talking past each other and making unspoken assumptions. For instance : If I presumed and imagined a scenario where the negative shell was somehow inherently rigid and unmoveable and static, then yes indeed a proton would float around within the shell without any location preference. You guys are presuming and imagining such a shell, while I am not.
That's a good start. It has nothing to do with immovable and static -- it only has to do with the shape remaining a spherical shell.
My shell has no self interaction and would collapse into the proton. It doesn't collapse however because it has orbital tangental velocity, and by the laws of orbital mechanics it has to remain in 'orbit' at a particular distance from the proton, a distance dependent on its velocity.
We have gone over this before. "orbits" are for an independent body moving around the nucleus. If the "electron" were a billion individual pieces, separately orbiting the nucleus, then they would indeed be subject to orbital mechanics.
Then you would have a host of new problems, like how is the total energy conserved when the pieces are independent? If independent, they would not end up in a shell, but instead a cloud, each with varying energy and ellipsoidal shape. If not independent, you need to invent magicalforces that pull the errant pieces back into a shell shape over time.
However, Mills does not propose independent bodies. Instead, he imagines a set of superconducting hoops, which themselves have no mass, but on which the "pieces" of the electron move. Mills does not state the properties of this the hoops (elasticity, rigidity, etc.), so we can assume they have none. They are simply a way for the electron "pieces" to go around in a loop. I think of it as water in a massless and infinitely-stretchy hula-hoop.
We are told that the electron density around the loop is constant, but I see no reason for this to be the case, unless, like water, the electron "pieces" are not compressible around the hoop.
Yes, the tangential motion of the electron "pieces" in the hula-hoop are what keeps everything from collapsing. We assume the hoop can expand and contract at need. The problem is, that neither a deformable loop, nor a rigid loop (with the exception of the one precessing case you found earlier) with a uniform electron-piece density around it, can be in a stable orbit. If multiple loops make a shell, then the shell does even worse at being stable. A rigid shell has no restoring force for the central proton, and a deformable shell (which I think it must be) is not stable either.
The problem is the inability for the "pieces" to change radius and phase independently. They are like pieces of a rotating linked chain, which is not stable once the attractive force goes off center. The pieces of a linked chain do not orbit.
And, frankly, how do these individual loops all share pieces of the overall energy under perturbation? There is no equation that gives stability or explains the dynamic behavior.
Not only that, the orbital velocity is declared to be inviolable, as a boundary condition. So if the electron shell is mildly perturbed the electron velocity must remain the same, and so by orbital mechanics its distance from the nucleus must remain the same. This means that if the electron is mildly perturbed the entire atom is perturbed and moves. Only when the disturbance to the shell exceeds the electromagnetic force between the proton and electron can the electron's orbit be broken and the electron escape the proton.
What you are describing makes sense to you, but doesn't really make sense. This is a classical situation. In real orbits, a perturbation causes a change, until a new equilibrium is found (a new elliptical orbit). In QM, a perturbation causes a chance of energy transfer, but the wave equation is quite stable (wave diffraction creates a new stable wave, and some entanglement with the perturbation). The orbitsphere, under perturbation, will not be stable.